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Folding transition and „ foldability ”. The phase transition. Density of water: temperature and pressure dependence. The phase diagram of water. H [J/mol]. C v [J/( mol*K )]. Temperature [ o C]. Temperature [ o C]. Vapor. Liquid water. Ice. „Chemical” view. N. U. Two-state model.
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The phase transition Density of water: temperature and pressure dependence The phase diagram of water
H [J/mol] Cv [J/(mol*K)] Temperature [oC] Temperature [oC] Vapor Liquid water Ice
„Chemical” view N U Two-state model N I U Three-state model
Priovalov and Mathakhadze, Adv. Prot. Chem., 47, 307-425 (1995)
Wild type Acid-denaturatedwildtype L16A mutant C-terminal peptide Religa et al., J. Mol. Biol., 333, 977-991 (2003)
Chodankhar et al., PRAMANA Journal of Physics, 71,1021-1025 (2008)
Staphylococcal protein A, B-domain (46 residues) • UNRES/MREMD simulations • Berendsen thermostat • 32 temperatures (250 K £T £500 K) • 4 trajectories/temperature (a total of 128 trajectories) • 28 million MD steps @Dt = 4.9 fs • Last 4 million steps for analysis • WHAM to compute ensemble averages Maisuradze et al., J. Am. Chem. Soc. 132,9444–9452 (2010)
Experimental structure of 1BDD (red) and most probable conformations (green) at T = 280 K C N
Variation of Ca rmsd distribution with temperature T = 280 K T = 300 K T = 320 K T = 310 K T = 315 K Probability T = 325 K T = 350 K Ca rmsd [Å]
Protein A @ the folding-transition temperature Experimental (referemce) rmsd=8.7 Å „mirror image” topology rmsd=9.8 Å „mirror image” topology rmsd=5.3 Å Native topology rmsd=9.5 Å Native topology
Ensemble-averaged contact-probability maps H-bonding contacts Experimental (reference) SC-SC contacts T=300 K T=325 K (Tf) T=350 K
Criteria of foldability • Gap criterion (Shakhnovich et al., 1994) • Large Tf/Tg, (folding to glass-transition temperature) ratio which is the principle of Z-score optimization (Wolynes et al., 1992) • Small (Tf-Tq)/Tq ratio (Tq being the hydrophobic collapse temperature; Thirumalai et al., 1996). Inverse proportionality found of the entropy of the excited states to Tf. • “Funnel sculpting” (Maritan and Seno, 2003 and Levitt et al., 2003) • Hierarchy
Energy spectra of a lattice model level 0 level 1 level 2 native tf – folding time (MFPT to the native structure) ts – residence time tfts Liwo et al., J. Phys. Chem. B, 108, 16934-16949 (2004)